Question

4. Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition (U) and an abraded condition (A). Use an appropriate test, to test if the average breaking load of a fabric under unabraded condition is higher than in the abraded condition, at 0.01 level. Fabric 3 4 5 6 7 8 1 2 U A 36.4 55.0 51.5 38.7 28.5 20.0 46.0 34.5 43.2 36.5 48.8 25.6 52.5 26.5 49.8 46.5 a) Write down the appropriate hypotheses in question. [2] b) Conduct the mentioned test and give a brief conclusion. [5]

Answer 1

Appropriate hypotheses is follows :

Ho : $\mu$ D = 0

Ha : $\mu$ D > 0

U	A	d = U - A	d-dbar	(d-dbar)^2
36.4	28.5	7.9	0.65	0.4225
55	20	35	27.75	770.0625
51.5	46	5.5	-1.75	3.0625
38.7	34.5	4.2	-3.05	9.3025
43.2	36.5	6.7	-0.55	0.3025
48.8	52.5	-3.7	-10.95	119.9025
25.6	26.5	-0.9	-8.15	66.4225
49.8	46.5	3.3	-3.95	15.6025
		58		985.08

sum of d = 58

n = 8

sum of (d-dbar)^2 = 985.08

  
985.08 V 8-1

s = 11.8627

Calculate T Value :

T 7.25 * V8 11.8627

T = 1.7286 ( calculated T value )

=n-1=8-1= 7

( value from T table )

to.01 3.499(table

Ho is passed and accepted. The average breaking load of a fabric under unabraded condition is higer than in the abraded conditions at 0.01 significance level